Question

Find the equation of the line which passes through the points (-1, 1) and (2, -4).

Answer 1

It is known that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is  \(y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)\)
Therefore, the equation of the line passing through the points (-1, 1) and (2, -4) is
\(y-1=\frac{-4-1}{2+1}\left(x+1\right)\)

\(y – 1 =\frac{ -5}{3} (x + 1)\)

\(3 (y – 1) = (-5) (x + 1)\)
\(3y – 3 = -5x – 5\)
\(3y – 3 + 5x + 5 = 0\)
\(i.e,5x + 3y + 2 = 0\)